Values of p between 1 and 2 are of most interest as these have
efficiency and robustness properties between the median (p = 1)
and the mean (p = 2).

The Pennecchi and Callegaro paper provides the following guidelines
for choosing a suitable value for p. Compute the sample
kurtosis,
\( \hat{k} \), of the sample observations (note that the standard
kurtosis formula should be used, not the version that subtracts 3 to
make the kurtosis of a normal distribution equal to 0). Then

\( \hat{k} \)
< 2.2

-

use the mid-range (i.e., p =
\( \infty \) )

2.2 ≤
\( \hat{k} \)
≤ 3

-

use the mean (i.e., p = 2)

3 <
\( \hat{k} \)
< 6

-

use p = 1.5

\( \hat{k} \) ≥ 6

-

use the median (i.e., p = 1)

Pennecchi and Callegaro propose the following as an estimate of
the asymptotic variance

\( \frac{m(2p - 2)}{\left( (p-1)m(p-2)\right) ^{2}}/n \)

where

\( m(r) = \frac{1}{n} \sum_{i=1}^{n}{|x_i - L_p(x_i)|^r} \)

Syntax 1:

LET <par> = LP LOCATION <y>
<SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
<par> is a parameter where the computed lp location
value is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

Use this syntax to compute the Lp location estimate.

Syntax 2:

LET <par> = VARIANCE OF LP LOCATION <y>
<SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
<par> is a parameter where the computed variance of the
lp location value is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

Use this syntax to compute the variance of the Lp location estimate.

Syntax 3:

LET <par> = SD OF LP LOCATION <y>
<SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
<par> is a parameter where the computed sd of the
lp location value is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

Use this syntax to compute the standard deviation of the Lp location
estimate.